Signals, Systems, and Signal Processing

This chapter introduces structures and structural interconnections for LTI systems and then considers several examples of digital filters. Examples include moving average filters, difference operators, and ideal lowpass filters. It is then shown how to convert lowpass filters into other types, such as highpass, bandpass, and so on, by use of simple transformations. Phase distortion is explained, and linear-phase digital filters are introduced, which do not create phase distortion. The use of digital filters in noise removal (denoising) is also demonstrated for 1D signals and 2D images. The filtering of an image into low and high-frequency subbands is demonstrated, and the motivation for subband decomposition in audio and image compression is explained. Finally, it is shown that the convolution operation can be represented as a matrix vector multiplication, where the matrix has Toeplitz structure. The matrix representation also shows us how to undo a filtering operation through a process called deconvolution.